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2023•INTERNATIONAL JOURNAL OF MATHEMATICS AND COMPUTER RESEARCHOpen access

D^DM- DISTANCE IN CYCLE RELATED GRAPHS

K. John Bosco, Sathija J Prathisa S K

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Abstract

For two vertices u and v of a graph G, the usual distance d (u, v), is the length of the shortest path between u and v. In this paper we introduced the concept of DdM- distance by considering the degrees of various vertices presented in the path, in addition to the length of the path. We study some properties with this new distance. We define the eccentricities of vertices, radius and diameter of G with respect to the DdM- distance. First we prove that the new distance is a metric on the set of vertices of G. We compare the usual, detour and DdM-distances of two vertices u,v of V.

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For two vertices u and v of a graph G, the usual distance d (u, v), is the length of the shortest path between u and v. In this paper we introduced the concept of DdM- distance by considering the degrees of various vertices presented in the path, in addition to the length of the path. We study some properties with this new distance. We define the eccentricities of vertices, radius and diameter of G with respect to the DdM- distance. First we prove that the new distance is a metric on the set of vertices of G. We compare the usual, detour and DdM-distances of two vertices u,v of V.

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Available abstract

For two vertices u and v of a graph G, the usual distance d (u, v), is the length of the shortest path between u and v. In this paper we introduced the concept of DdM- distance by considering the degrees of various vertices presented in the path, in addition to the length of the path. We study some properties with this new distance. We define the eccentricities of vertices, radius and diameter of G with respect to the DdM- distance. First we prove that the new distance is a metric on the set of vertices of G. We compare the usual, detour and DdM-distances of two vertices u,v of V.

Key concepts: Distance, Combinatorics, Mathematics, Metric dimension, Path graph, Shortest path problem, Path (computing), RADIUS

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