5 papers
k-Mutual Visibility in Graphs
Tonny K B, Shikhi M
In this paper, we introduce the notion of -mutual visibility, a relaxation of classical mutual visibility in which every pair of selected vertices is joined by a shortest path c…
Mutual-Visibility of Tree and Its Line Graphs
Tonny K B, Shikhi M
In this paper, we present a complete characterization of mutual-visibility sets in trees. It is shown that a subset is a mutual-visibility set of a tree if and only if it c…
Visibility Polynomial of Some Graph Classes
Tonny K B, Shikhi M
Mutual visibility in graphs provides a framework for analysing how vertices can observe one another along shortest paths free of internal obstructions. The visibility polynomial, w…
Visibility polynomial of corona of two graphs
Tonny K B, Shikhi M
In multiagent systems, effective coordination, coverage, and communication often rely on the concept of visibility between agents or nodes within the system. Graph-theoretically, f…
On the Visibility Polynomial of Graphs
Tonny K B, Shikhi M
Let G(V,E) be a simple graph and let X subset of V. Two vertices u and v are said to be X-visible if there exists a shortest u,v-path P such that V(P) intersection X is a subset of…