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Journal articles on the topic 'Geodetic graphs'

Author: Grafiati

Published: 5 June 2025

Last updated: 15 July 2025

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1

Gajavalli, S., and A. Berin Greeni. "On Geodesic Convexity in Mycielskian of Graphs." Journal of Advanced Computational Intelligence and Intelligent Informatics 27, no. 1 (2023): 119–23. http://dx.doi.org/10.20965/jaciii.2023.p0119.

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The convexity induced by the geodesics in a graph G is called the geodesic convexity of G. Mycielski graphs preserve the property of being triangle-free and many parameters such as power domination number, coloring number, determining number and recently general position number have been determined for them. In this work, we determine the geodesic convexity parameters viz., convexity, geodetic iteration, geodetic, and hull numbers for Mycielski graphs for which the underlying graphs considered are path, cycle, star, and complete graph.

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2

González, Yero, and Magdalena Lemńska. "Convex dominating-geodetic partitions in graphs." Filomat 30, no. 11 (2016): 3075–82. http://dx.doi.org/10.2298/fil1611075g.

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The distance d(u,v) between two vertices u and v in a connected graph G is the length of a shortest u-v path in G. A u-v path of length d(u,v) is called u-v geodesic. A set X is convex in G if vertices from all a -b geodesics belong to X for every two vertices a,b?X. A set of vertices D is dominating in G if every vertex of V-D has at least one neighbor in D. The convex domination number con(G) of a graph G equals the minimum cardinality of a convex dominating set in G. A set of vertices S of a graph G is a geodetic set of G if every vertex v ? S lies on a x-y geodesic between two vertices x,y

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3

Ge, Huifen, Zhao Wang, and Jinyu Zou. "Strong Geodetic Number in Some Networks." Journal of Mathematics Research 11, no. 2 (2019): 20. http://dx.doi.org/10.5539/jmr.v11n2p20.

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A vertex subset S of a graph is called a strong geodetic set if there exists a choice of exactly one geodesic for each pair of vertices of S in such a way that these (|S| 2) geodesics cover all the vertices of graph G. The strong geodetic number of G, denoted by sg(G), is the smallest cardinality of a strong geodetic set. In this paper, we give an upper bound of strong geodetic number of the Cartesian product graphs and study this parameter for some Cartesian product networks.

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Ganesamoorthy, K., and D. Jayanthi. "Extreme Outer Connected Geodesic Graphs." Proyecciones (Antofagasta) 43, no. 1 (2024): 103–17. http://dx.doi.org/10.22199/issn.0717-6279-5401.

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For a connected graph G of order at least two, a set S of vertices in a graph G is said to be an outer connected geodetic set if S is a geodetic set of G and either S = V or the subgraph induced by V − S is connected. The minimum cardinality of an outer connected geodetic set of G is the outer connected geodetic number of G and is denoted by goc(G). The number of extreme vertices in G is its extreme order ex(G). A graph G is said to be an extreme outer connected geodesic graph if goc(G) = ex(G). It is shown that for every pair a, b of integers with 0 ≤ a ≤ b and b ≥ 2, there exists a connected

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5

Titus, P., and A. P. Santhakumaran. "Extreme Monophonic Graphs and Extreme Geodesic Graphs." Tamkang Journal of Mathematics 47, no. 4 (2016): 393–404. http://dx.doi.org/10.5556/j.tkjm.47.2016.2045.

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For a connected graph $G=(V,E)$ of order at least two, a chord of a path $P$ is an edge joining two non-adjacent vertices of $P$. A path $P$ is called a monophonic path if it is a chordless path. A monophonic set of $G$ is a set $S$ of vertices such that every vertex of $G$ lies on a monophonic path joining some pair of vertices in $S$. The monophonic number of $G$ is the minimum cardinality of its monophonic sets and is denoted by $m(G)$. A geodetic set of $G$ is a set $S$ of vertices such that every vertex of $G$ lies on a geodesic joining some pair of vertices in $S$. The geodetic number of

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6

Adolfo, Niña Jeane, Imelda Aniversario, and Ferdinand Jamil. "Closed Geodetic Hop Domination in Graphs." European Journal of Pure and Applied Mathematics 17, no. 3 (2024): 1618–36. http://dx.doi.org/10.29020/nybg.ejpam.v17i3.5241.

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Let G be a simple, undirected and connected graph. A subset S ⊆ V (G) is a geodetic cover of G if IG[S] = V (G), where IG[S] is the set of all vertices of G lying on any geodesic between two vertices in S. A geodetic cover S of G is a closed geodetic cover if the vertices in S are sequentially selected as follows: Select a vertex v1 and let S1 = {v1}. If G is nontrivial, select a vertex v2 ̸= v1 and let S2 = {v1, v2}. Where possible, for i ≥ 3, successively select vertex vi ∈/ IG[Si−1] and let Si = {v1, v2, ..., vi}. Then there exists a positive integer k such that Sk = S. A geodetic cover S o

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7

Catian, Dyjay Bill, Imelda Aniversario, and Ferdinand Jamil. "On Minimal Geodetic Hop Domination in Graphs." European Journal of Pure and Applied Mathematics 17, no. 3 (2024): 1737–50. http://dx.doi.org/10.29020/nybg.ejpam.v17i3.5251.

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Let $G$ be a nontrivial connected graph with vertex set $V(G)$. A set $S \subseteq V(G)$ is a geodetic hop dominating set of $G$ if the following two conditions hold for each $x\in V(G)\setminus S$: $(1)$ $x$ lies in some $u$-$v$ geodesic in $G$ with $u,v\in S$, and $(2)$ $x$ is of distance $2$ from a vertex in $S$. The minimum cardinality $\gamma_{hg}(G)$ of a geodetic hop dominating set of $G$ is the geodetic hop domination number of $G$. A geodetic hop dominating set $S$ is a minimal geodetic hop dominating set if $S$ does not contain a proper subset that is itself geodetic hop dominating s

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8

SANTHAKUMARAN, A. P. "EXTREME STEINER GRAPHS." Discrete Mathematics, Algorithms and Applications 04, no. 02 (2012): 1250029. http://dx.doi.org/10.1142/s1793830912500292.

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For a connected graph G of order p ≥ 2 and a set W ⊆ V(G), a tree T contained in G is a Steiner tree with respect to W if T is a tree of minimum order with W ⊆ V(T). The set S(W) consists of all vertices in G that lie on some Steiner tree with respect to W. The set W is a Steiner set for G if S(W) = V(G). The Steiner number s(G) of G is the minimum cardinality of its Steiner sets and any Steiner set of cardinality s(G) is a minimum Steiner set of G. A geodetic set of G is a set S of vertices such that every vertex of G is contained in a geodesic joining some pair of vertices of S. The geodetic

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9

Nebeský, Ladislav. "A characterization of geodetic graphs." Czechoslovak Mathematical Journal 45, no. 3 (1995): 491–93. http://dx.doi.org/10.21136/cmj.1995.128536.

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10

Gnana Santhiyagu, G. Micheal Antony, S. Balamurugan, and R. Arul Ananthan. "Changing and Unchanging the Geodetic Number: Edge Removal." Mapana Journal of Sciences 22, no. 4 (2024): 115–21. https://doi.org/10.12723/mjs.67.8.

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Let S be a collection of elements in a vertex set V. If every vertex in a graph G falls on a geodesic connecting two vertices from S, then that graph is said to be a geodesic set. g(G) is the smallest cardinality of the geodesic subset of a graph G is known as the geodetic number. This study investigates how the removal of an edge affects some unique families of graphs' geodetic numbers.

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Artigas, Danilo, Simone Dantas, and Mitre Dourado. "Geodesic Convexity of graphs: partition and geodetic sets." Cadernos do IME - Série Informática 47 (October 18, 2022): 11–13. http://dx.doi.org/10.12957/cadinf.2022.70578.

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12

Onur, Şeyma, and Gökşen Bacak Turan. "Geodetic Domination Integrity of Thorny Graphs." Journal of New Theory, no. 46 (March 28, 2024): 99–109. http://dx.doi.org/10.53570/jnt.1442636.

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The concept of geodetic domination integrity is a crucial parameter when examining the potential damage to a network. It has been observed that the removal of a geodetic set from the network can increase its vulnerability. This study explores the geodetic domination integrity parameter and presents general results on the geodetic domination integrity values of thorn ring graphs, $n$-sunlet graphs, thorn path graphs, thorn rod graphs, thorn star graphs, helm graphs, $E_p^t$ tree graphs, dendrimer graphs, spider graphs, and bispider graphs, which are the frequently used graph classes in the lite

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13

Rehmani, Sameeha. "PERFECT S-GEODETIC FUZZY GRAPHS." International Journal of Advanced Research 13, no. 01 (2025): 695–98. https://doi.org/10.21474/ijar01/20245.

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This study introduces the concept of a Pseudo s-geodetic set within the context of fuzzy graphs. This set comprises all nodes that are not members of any s-geodetic basis for a given fuzzy graph G. The size of this set is termed the Pseudo s-geodetic number of G. We specifically define fuzzy graphs possessing a Pseudo s-geodetic number of zero as Perfect s-geodetic fuzzy graphs. Several examples of such graphs are provided. Furthermore, we demonstrate that complete fuzzy graphs with two nodes, as well as fuzzy cycles where each arc has identical strength, fall under the category of Perfect s-g

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14

Manuel, Paul, Sandi Klavžar, Antony Xavier, Andrew Arokiaraj, and Elizabeth Thomas. "Strong edge geodetic problem in networks." Open Mathematics 15, no. 1 (2017): 1225–35. http://dx.doi.org/10.1515/math-2017-0101.

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Abstract Geodesic covering problems form a widely researched topic in graph theory. One such problem is geodetic problem introduced by Harary et al. [Math. Comput. Modelling, 1993, 17, 89-95]. Here we introduce a variation of the geodetic problem and call it strong edge geodetic problem. We illustrate how this problem is evolved from social transport networks. It is shown that the strong edge geodetic problem is NP-complete. We derive lower and upper bounds for the strong edge geodetic number and demonstrate that these bounds are sharp. We produce exact solutions for trees, block graphs, silic

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15

Hamja, Jamil, Imelda S. Aniversario, and Helen M. Rara. "On Weakly Connected Closed Geodetic Domination in Graphs Under Some Binary Operations." European Journal of Pure and Applied Mathematics 15, no. 2 (2022): 736–52. http://dx.doi.org/10.29020/nybg.ejpam.v15i2.4356.

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Let G be a simple connected graph. For S ⊆ V (G), the weakly connected closed geodetic dominating set S of G is a geodetic closure IG[S] which is between S and is the set of all vertices on geodesics (shortest path) between two vertices of S. We select vertices of Gsequentially as follows: Select a vertex v1 and let S1 = {v1}. Select a vertex v2 ̸= v1 and let S2 = {v1, v2}. Then successively select vertex vi ∈/ IG[Si−1] and let Si = {v1, v2, ..., vi} for i = 1, 2, ..., k until we select a vertex vk in the given manner that yields IG[Sk] = V (G). Also, the subgraph weakly induced ⟨S⟩w by S is c

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16

Mulloor, John Joy, and V. Sangeetha. "Restrained geodetic domination in graphs." Discrete Mathematics, Algorithms and Applications 12, no. 06 (2020): 2050084. http://dx.doi.org/10.1142/s1793830920500846.

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Let [Formula: see text] be a graph with edge set [Formula: see text] and vertex set [Formula: see text]. For a connected graph [Formula: see text], a vertex set [Formula: see text] of [Formula: see text] is said to be a geodetic set if every vertex in [Formula: see text] lies in a shortest path between any pair of vertices in [Formula: see text]. If the geodetic set [Formula: see text] is dominating, then [Formula: see text] is geodetic dominating set. A vertex set [Formula: see text] of [Formula: see text] is said to be a restrained geodetic dominating set if [Formula: see text] is geodetic,

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17

Anoche, Jesica, Imelda Aniversario, and Catherine I. Merca. "Path-Induced Closed Geodetic Domination of Some Common Graphs and Edge Corona of Graphs." European Journal of Pure and Applied Mathematics 16, no. 1 (2023): 169–79. http://dx.doi.org/10.29020/nybg.ejpam.v16i1.4506.

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Let G be a connected graph of order n and S ⊆ V (G). A closed geodetic cover S of Gis a path-induced closed geodetic dominating set of a graph G if a subgraph <S> has a Hamiltonianpath and S is a dominating set of G. The minimum cardinality of a path-induced closed geodeticdominating set is called path-induced closed geodetic domination number of G. This study presentsthe characterization of the path-induced closed geodetic dominating sets of some common graphsand edge corona of two graphs. The path-induced closed geodetic domination numbers of thesegraphs are also determined.

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18

C. Jayasekaran and A. Sheeba. "Relatively prime geodetic number of graphs." Malaya Journal of Matematik 8, no. 04 (2020): 2302–5. http://dx.doi.org/10.26637/mjm0804/0170.

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In this paper we introduce relatively prime geodetic number of a graph \(G\). Let \(G\) be a connected graph. A set \(S \subseteq V\) is said to be a relatively prime geodetic set if it is a geodetic set with at least three elements and the shortest distance between any two pairs of vertices in \(S\) is relatively prime. The relatively prime geodetic set of \(G\) is denoted by \(g_{r p}(G)\)-set. The cardinality of a minimum relatively prime geodetic set is the relatively prime geodetic number and it is denoted \(g_{r p}(G)\).

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19

Chartrand, Gary, Frank Harary, and Ping Zhang. "Geodetic sets in graphs." Discussiones Mathematicae Graph Theory 20, no. 1 (2000): 129. http://dx.doi.org/10.7151/dmgt.1112.

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20

Buckley, Fred, and Frank Harary. "GEODETIC GAMES FOR GRAPHS." Quaestiones Mathematicae 8, no. 4 (1985): 321–34. http://dx.doi.org/10.1080/16073606.1985.9631921.

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21

Scapellato, Raffaele. "On F-geodetic graphs." Discrete Mathematics 80, no. 3 (1990): 313–25. http://dx.doi.org/10.1016/0012-365x(90)90250-l.

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22

Rhodes, Frank, and Robert A. Melter. "Geodetic metrizations of graphs." Discrete Mathematics 194, no. 1-3 (1999): 267–79. http://dx.doi.org/10.1016/s0012-365x(98)00153-8.

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23

Joel, T. Iwin, and E. Ebin Raja Merly. "Geodetic Decomposition of Graphs." Journal of Computer and Mathematical Sciences 9, no. 7 (2018): 829–33. http://dx.doi.org/10.29055/jcms/818.

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24

Chang, Gerard J., Li-Da Tong, and Hong-Tsu Wang. "Geodetic spectra of graphs." European Journal of Combinatorics 25, no. 3 (2004): 383–91. http://dx.doi.org/10.1016/j.ejc.2003.09.010.

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25

Koolen, J. H. "On uniformly geodetic graphs." Graphs and Combinatorics 9, no. 2-4 (1993): 325–33. http://dx.doi.org/10.1007/bf02988320.

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26

Quije, Clint Joy, Rochelleo Mariano, and Eman Ahmad. "Edge Geodetic Dominating Sets of Some Graphs." European Journal of Pure and Applied Mathematics 18, no. 1 (2025): 5555. https://doi.org/10.29020/nybg.ejpam.v18i1.5555.

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Let $G$ be a simple graph. A subset $D$ of vertices in $G$ is a dominating set of $G$ if every vertex not in $D$ has at least one neighbor in $D$. The domination number $\gamma(G)$ of $G$ is the minimum cardinality of a dominating set of $G$. An edge geodetic set of $G$ is a set $S \subseteq V(G)$ such that every edge of $G$ is contained in a geodetic joining some pair of vertices in $S$. The edge geodetic number $g_e(G)$ of $G$ is the minimum cardinality of edge geodetic set. A set of vertices $S$ in $G$ is an edge geodetic dominating set of $G$ if $S$ is both an edge geodetic set and a domin

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27

A. Merin Sherly, P. Arul Paul Sudhahar,. "Split Geodetic Dominating Sets in Path Graphs." Tuijin Jishu/Journal of Propulsion Technology 44, no. 3 (2023): 1496–99. http://dx.doi.org/10.52783/tjjpt.v44.i3.523.

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Let be the family of split geodetic dominating sets of the path graph . with cardinality i and let . Then the split geodetic polynomial of is defined as = , where is the split geodetic domination number of .In this paper we have determined the family of split geodetic dominating sets of the path graph with cardinality .Also , we have obtained the recursive formula to derive the split geodetic domination polynomials of paths and also obtain some properties of this polynomial.

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28

Friedler, Louis M., Rommy Márquez, and Jake A. Soloff. "Products of geodesic graphs and the geodetic number of products." Discussiones Mathematicae Graph Theory 35, no. 1 (2015): 35. http://dx.doi.org/10.7151/dmgt.1774.

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29

Nebeský, Ladislav. "The interval function of a connected graph and a characterization of geodetic graphs." Mathematica Bohemica 126, no. 1 (2001): 247–54. http://dx.doi.org/10.21136/mb.2001.133909.

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Saromines, Chrisley Jade, and Sergio Canoy Jr. "Another Look at Geodetic Hop Domination in a Graph." European Journal of Pure and Applied Mathematics 16, no. 3 (2023): 1568–79. http://dx.doi.org/10.29020/nybg.ejpam.v16i3.4810.

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Let $G$ be an undirected graph with vertex and edge sets $V(G)$ and $E(G)$, respectively. A subset $S$ of vertices of $G$ is a geodetic hop dominating set if it is both a geodetic and a hop dominating set. The geodetic hop domination number of $G$ is the minimum cardinality among all geodetic hop dominating sets in $G$. Geodetic hop dominating sets in a graph resulting from the join of two graphs have been characterized. These characterizations have been used to determine the geodetic hop domination number of the graphs considered. A realization result involving the hop domination number and g

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31

Leema, J. Anne Mary, V. M. Arul Flower Mary, P. Titus, and B. Uma Devi. "The upper geodetic vertex covering number of a graph." Proyecciones (Antofagasta) 43, no. 6 (2024): 1097–112. http://dx.doi.org/10.22199/issn.0717-6279-5101.

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A set S ⊆ V (G) is a geodetic vertex cover of G if S is both a geodetic set and a vertex cover of G. The minimum cardinality of a geodetic vertex cover of G is defined as the geodetic vertex covering number of G and is denoted by gα(G) . A geodetic vertex cover S in a connected graph G is called a minimal geodetic vertex cover of G if no proper subset of S is a geodetic vertex cover of G. The upper geodetic vertex covering number g+α(G) of G is the maximum cardinality of a minimal geodetic vertex cover of G. Some general properties satisfied by the upper geodetic vertex covering number of a

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32

Iršič, Vesna, and Sandi Klavžar. "Strong geodetic problem on Cartesian products of graphs." RAIRO - Operations Research 52, no. 1 (2018): 205–16. http://dx.doi.org/10.1051/ro/2018003.

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The strong geodetic problem is a recent variation of the geodetic problem. For a graph G, its strong geodetic number sg(G) is the cardinality of a smallest vertex subset S, such that each vertex of G lies on a fixed shortest path between a pair of vertices from S. In this paper, the strong geodetic problem is studied on the Cartesian product of graphs. A general upper bound for sg(G □ H) is determined, as well as exact values for Km □ Kn, K1,k □ Pl, and prisms over Kn–e. Connections between the strong geodetic number of a graph and its subgraphs are also discussed.

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Ahangar Abdollahzadeh, Hossein, Saeed Kosari, Seyed Sheikholeslami, and Lutz Volkmann. "Graphs with large geodetic number." Filomat 29, no. 6 (2015): 1361–68. http://dx.doi.org/10.2298/fil1506361a.

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Deepa, Mathew, Antony Xavier D., and Theresal Santiagu. "k-Geodetic propagation in graphs." Malaya Journal of Matematik S, no. 1 (2020): 6–10. http://dx.doi.org/10.26637/mjm0s20/0002.

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Deepa, Mathew, Antony Xavier D., Theresal Santiagu, and Arul Amirtha Raja S. "Geodetic landmark number of graphs." Malaya Journal of Matematik S, no. 1 (2020): 76–80. http://dx.doi.org/10.26637/mjm0s20/0015.

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Fraenkel, A. S., and F. Harary. "Geodetic contraction games on graphs." International Journal of Game Theory 18, no. 3 (1989): 327–38. http://dx.doi.org/10.1007/bf01254296.

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Bedo, Marcos, João V. S. Leite, Rodolfo A. Oliveira, and Fábio Protti. "Geodetic convexity and kneser graphs." Applied Mathematics and Computation 449 (July 2023): 127964. http://dx.doi.org/10.1016/j.amc.2023.127964.

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SANTHAKUMARAN, A. P., T. JEBARAJ, and S. V. ULLAS CHANDRAN. "THE LINEAR GEODETIC NUMBER OF A GRAPH." Discrete Mathematics, Algorithms and Applications 03, no. 03 (2011): 357–68. http://dx.doi.org/10.1142/s1793830911001279.

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For a connected graph G of order n, an ordered set S = {u1, u2, …, uk} of vertices in G is a linear geodetic set of G if for each vertex x in G, there exists an index i, 1 ≤ i < k such that x lies on a ui - ui + 1 geodesic on G, and a linear geodetic set of minimum cardinality is the linear geodetic number gl(G). The linear geodetic numbers of certain standard graphs are obtained. It is shown that if G is a graph of order n and diameter d, then gl(G) ≤ n - d + 1 and this bound is sharp. For positive integers r, d and k ≥ 2 with r < d ≤ 2r, there exists a connected graph G with rad G = r,

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Santhakumaran, A. P., and J. John. "The upper connected edge geodetic number of a graph." Filomat 26, no. 1 (2012): 131–41. http://dx.doi.org/10.2298/fil1201131s.

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For a non-trivial connected graph G, a set S ? V (G) is called an edge geodetic set of G if every edge of G is contained in a geodesic joining some pair of vertices in S. The edge geodetic number g1(G) of G is the minimum order of its edge geodetic sets and any edge geodetic set of order g1(G) is an edge geodetic basis. A connected edge geodetic set of G is an edge geodetic set S such that the subgraph G[S] induced by S is connected. The minimum cardinality of a connected edge geodetic set of G is the connected edge geodetic number of G and is denoted by g1c(G). A connected edge geodetic set o

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Abudayah, Mohammad, Omar Alomari, and Hassan Ezeh. "Geodetic Number of Powers of Cycles." Symmetry 10, no. 11 (2018): 592. http://dx.doi.org/10.3390/sym10110592.

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The geodetic number of a graph is an important graph invariant. In 2002, Atici showed the geodetic set determination of a graph is an NP-Complete problem. In this paper, we compute the geodetic set and geodetic number of an important class of graphs called the k-th power of a cycle. This class of graphs has various applications in Computer Networks design and Distributed computing. The k-th power of a cycle is the graph that has the same set of vertices as the cycle and two different vertices in the k-th power of this cycle are adjacent if the distance between them is at most k.

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Xaviour, X. Lenin, and S. Robinson Chellathurai. "Geodetic global domination in corona and strong product of graphs." Discrete Mathematics, Algorithms and Applications 12, no. 04 (2020): 2050043. http://dx.doi.org/10.1142/s1793830920500433.

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A set S of vertices in a connected graph [Formula: see text] is called a geodetic set if every vertex not in [Formula: see text] lies on a shortest path between two vertices from [Formula: see text]. A set [Formula: see text] of vertices in [Formula: see text] is called a dominating set of [Formula: see text] if every vertex not in [Formula: see text] has at least one neighbor in [Formula: see text]. A set [Formula: see text] is called a geodetic global dominating set of [Formula: see text] if [Formula: see text] is both geodetic and global dominating set of [Formula: see text]. The geodetic g

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Mathew, Deepa, and D. Antony Xavier. "STRONG DOUBLY GEODETIC PROBLEM ON GRAPHS." JP Journal of Algebra, Number Theory and Applications 49, no. 1 (2021): 23–49. http://dx.doi.org/10.17654/nt049010023.

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Cornelsen, Sabine, Maximilian Pfister, Henry Förster, et al. "Drawing Shortest Paths in Geodetic Graphs." Journal of Graph Algorithms and Applications 26, no. 3 (2022): 353–61. http://dx.doi.org/10.7155/jgaa.00598.

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Jamil, Ferdinand P., and Hearty M. Nuenay. "On minimal geodetic domination in graphs." Discussiones Mathematicae Graph Theory 35, no. 3 (2015): 403. http://dx.doi.org/10.7151/dmgt.1803.

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45

John, J., and D. Stalin. "Edge geodetic self-decomposition in graphs." Discrete Mathematics, Algorithms and Applications 12, no. 05 (2020): 2050064. http://dx.doi.org/10.1142/s1793830920500640.

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Abstract:

Let [Formula: see text] be a simple connected graph of order [Formula: see text] and size [Formula: see text]. A decomposition of a graph [Formula: see text] is a collection of edge-disjoint subgraphs [Formula: see text] of [Formula: see text] such that every edge of [Formula: see text] belongs to exactly one [Formula: see text]. The decomposition [Formula: see text] of a connected graph [Formula: see text] is said to be an edge geodetic self-decomposition if [Formula: see text] for all [Formula: see text]. Some general properties satisfied by this concept are studied.

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46

Ahangar Abdollahzadeh, Hossein. "Graphs with large total geodetic number." Filomat 31, no. 13 (2017): 4297–304. http://dx.doi.org/10.2298/fil1713297a.

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Nieminen, J., and M. Peltola. "The minumum geodetic communication overlap graphs." Applied Mathematics Letters 11, no. 2 (1998): 99–102. http://dx.doi.org/10.1016/s0893-9659(98)00018-4.

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Ahangar, Hossein Abdollahzadeh, and Maryam Najimi. "Total Restrained Geodetic Number of Graphs." Iranian Journal of Science and Technology, Transactions A: Science 41, no. 2 (2017): 473–80. http://dx.doi.org/10.1007/s40995-017-0158-4.

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Venkanagouda, M. Goudar, and K. L. Venkanagouda. "Some Geodetic Parameters of Snake Graphs." Journal of Computer and Mathematical Sciences 9, no. 11 (2018): 1585–600. http://dx.doi.org/10.29055/jcms/901.

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Bhavyavenu, K. L., and Venkanagouda M. Goudar. "Doubly connected geodetic number of graphs." Malaya Journal of Matematik 06, no. 03 (2018): 626–31. http://dx.doi.org/10.26637/mjm0603/0025.

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