Let G be a simple graph with vertex set V (G)={v 1, v 2,…, vn}. The Sombor matrix of G,
denoted by A SO (G), is defined as the n× n matrix whose (i, j)-entry is di 2+ dj 2 if vi and vj …

Let G be a simple graph of order n. The domination polynomial of G is the polynomial D (G,
x)=\sum_ {i=\gamma (G)}^ nd (G, i) x^ i, where d (G, i) is the number of dominating sets of G …

We establish a formula for the number of 4-matchings in triangular-free graph with respect to
the number of vertices, edges, degrees and 4-cycles. Using this formula, it is proved that the …

Let $ G $ be a simple graph with vertex set $ V (G)=\{v_1, v_2,\ldots, v_n\} $. The elliptic
Sombor matrix of $ G $, denoted by $ A_ {ESO}(G) $, is defined as the $ n\times n $ matrix …

Number of 5-Matchings in Graphs Page 1 Number of 5-Matchings in Graphs R. Vesalian , F.Asgari
Department of Mathematics, Mahshahr Branch, Islamic Azad University, Mahshahr, Iran (Received …

A connected $ k $-chromatic graph $ G $ is said to be {\it double-critical} if for all edges $ uv
$ of $ G $ the graph $ Guv $ is $(k-2) $-colourable. A longstanding conjecture of Erd\H {o} s …

A cube factorization of the complete graph on n vertices, Kn, is a 3‐factorization of Kn in
which the components of each factor are cubes. We show that there exists a cube …

arXiv:1407.5480v1 [math.CO] 21 Jul 2014 Page 1 arXiv:1407.5480v1 [math.CO] 21 Jul 2014
A note on m-factorizations of complete multigraphs arising from designs Gy. Kiss† ∗ and C …

Let $ G $ be a simple graph of order $ n $. The energy $ E (G) $ of the graph $ G $ is the
sum of the absolute values of the eigenvalues of $ G $. The Randi\'{c} matrix of $ G …

The coalition in a graph $ G $ consists of two disjoint sets of vertices $ V_ {1} $ and $ V_ {2}
$, neither of which is a dominating set but whose union $ V_ {1}\cup V_ {2} $, is a …