Radio Labeling and Radio Number for Generalized Caterpillar Graphs

Abstract

where diam(G) and d (u, v) are diameter and distance between u and v in graph G respectively. The radio number rn(G) of G is the smallest number k such that G has radio labeling with max{g(v) : v ∈ V (G)} = k. We investigate radio number for some families of generalized caterpillar graphs.

Porous exponential domination number of some graphs

“…▪ Definition 5 (Nazeer et al [17]). The graph C (m, 0) P n is generalized caterpillar derived from P n by attaching m vertices of degree one to each vertex of degree two of P n .…”

Fuzzy Radio Reciprocal L-Labeling on Certain Chemical Graphs

“…Tom & sunith (2015) proved strong sum distance in fuzzy graphs is metric and the distance of a fuzzy graph is greater than or equal to its radius of fuzzy graph and less than or equal radius with multiple 2 of fuzzy graph (10) . Nazeer et al (2016) discussed the radio labeling of Generalized Caterpillar graphs C(m,1)Pn, which is obtained from Pn by attaching m vertices of degree two to each vertex of degree two of Pn. They found a generalized result for radio labelling number in Generalized Caterpillar graphs (11) .…”

“…Nazeer et al (2016) discussed the radio labeling of Generalized Caterpillar graphs C(m,1)Pn, which is obtained from Pn by attaching m vertices of degree two to each vertex of degree two of Pn. They found a generalized result for radio labelling number in Generalized Caterpillar graphs (11) . Mahapatra et al (2019) introduced radio fuzzy graph.…”