Distance two labeling of certain snake graphs

Abstract

An L(2,1) labeling (or) distance two labeling of a graph G is a function f from the vertex set V(G) to the set of all non-negative integers such that |f(x) −f(y)|≥ 2 if d(x,y) =1 and |f(x) −f(y)|≥ 1 if d(x, y) = 2. The L(2, 1) labeling number (G) of G is the smallest number k such that G has an L(2,1) labeling with max{f(v), v∈ V(G)} = k. In this paper we determine the L(2,1) labeling number (G) for the line graph of triangular snake graph and spiked snake graph.

The bounds for the distance two labelling and radio labelling of nanostar tree dendrimer

“…In addition, Sakai [10] obtained the distance two labelling of chordal graphs. Smitha and Thirusangu [11] proved the results for the quadrilateral snake 𝑄 𝑛 as 8 and for the alternate quadrilateral snake graph 𝑄 𝑛 as 5 for 𝑛 ≥ 2. Kujur et al [12] proved that 𝜆 2,1 (𝐵 𝑚,𝑛 ) ≤ 13, where the bloom graph is 𝐵 𝑚,𝑛 (𝑛, 𝑚 > 2).…”

Radial radio number of chess board graph and king’s graph

“…Prajapati and Patel [6] obtained the L(2, 1) labeling number of crown graph and line graph of armed crown graph. Smitha and Thirusangu [7] determined the L(2, 1) labeling of cycle related graphs. Besides, L(2, 1) labeling of unigraph was computed by Calamoneri and Petreschi [8].…”

Independent Domination Number in Triangular & Quadrilateral Snake graph

“…Definition 8. [7] Quadrilateral snake: A quadrilateral snake is obtained from a path by joining to new vertices respectively and joining the vertices for i=1,2,...n-1. That is every edge of a path is replaced by a cycle .…”

“…Definition 10. [7] Double Quadrilateral snake: A double quadrilateral snake is obtained from two quadrilateral snakes that have a common path. Definition 11.…”

“…Definition 11. [7] of a path by a triangle . Now we select the vertices for the set S (independent domination set) from a graph , in such a way that each vertex in S is adjacent to atleast one vertex in V-S and that each vertex in S is independent.…”