A new generalization of Fiedler's lemma is obtained by introducing the concept main function a matrix. As applications, universal spectra H-join any graphs (possibly non-regular) and adjacency H-generalized join constrained (arbitrary) vertex subsets are obtained. The generalized corona deduced from graphs. Also, construction infinitely many pairs non-regular cospectral provided.

The Wiener index is a graph invariant that has found extensive application in chemistry. In addition to that a generating function, which was called the Wiener polynomial, who’s derivate is a q-analog of the Wiener index was defined. In an article, Sagan, Yeh and Zhang in [The Wiener Polynomial of a graph, Int. J. Quantun Chem., 60 (1996), 959969] attained what graph operations do to the Wiene...

Abstract In this paper, the exact formulae for the Harary indices of join, disjunction, symmetric difference, strong product of graphs are obtained. Also, the Schultz and modified Schultz indices of join and strong product of graphs are computed. We apply some of our results to compute the Harary, Schultz and modified Schultz indices of fan graph, wheel graph, open fence and closed fence graphs.

A fuzzy graph can be obtained from two given fuzzy graphs using union and join. In this paper, we find the degree of an edge in fuzzy graphs formed by these operations in terms of the degree of edges in the given fuzzy graphs in some particular cases. 1. Introduction Fuzzy graph theory was introduced by Azriel Rosenfeld in 1975 [4]. Though it is very young, it has been growing fast and has nume...

We study the spectrum of join several circulant matrices. apply our results to compute explicitly certain graphs obtained by joining graphs.

bandwidth labelling is a well known research area in graph theory. we provide a new proof that the bandwidth of mobius ladder is 4, if it is not a $k_{4}$, and investigate the bandwidth of a wider class of mobius graphs of even strips.

Let $$F_1$$ and $$F_2$$ be two disjoint graphs. The union $$F_1\cup F_2$$ is a graph with vertex set $$V(F_1)\cup V(F_2)$$ edge $$E(F_1)\cup E(F_2)$$ , the join $$F_1+F_2$$ E(F_2)\cup \{xy\;|\; x\in V(F_1)\hbox { } y\in V(F_2)\}$$ . In this paper, we present characterization to $$(P_5, K_1\cup K_3)$$ -free graphs, prove that $$\chi (G)\le 2\omega (G)-1$$ if G -free. Based on result, further $$ ...