Graphs considered in this paper are simple finite undirected graphs without loops or multiple edges. A where each vertex has degree 3 is called cubic graphs. graphs, that is, 1-connected bridge graph traceable if its contains Hamiltonian path otherwise, non-traceable. In paper, we introduce a new family of Non-Traceable Cubic Bridge Graph (NTCBG) satisfy the conjecture Zoeram and Yaqubi (2017)....

Given a set ξ = {H1,H2, · · ·} of connected non acyclic graphs, a ξ-free graph is one which does not contain any member of ξ as copy. Define the excess of a graph as the difference between its number of edges and its number of vertices. Let Ŵk,ξ be theexponential generating function (EGF for brief) of connected ξ-free graphs of excess equal to k (k ≥ 1). For each fixed ξ, a fundamental differen...

Objectives: To find the connected restrained detour number for standard graphs and mesh graphs. Methods: By determining set with minimum cardinality, of a graph is investigated. Findings: We study that altered when we add pendent vertices. The maximum degree vertices are deleted computed. Novelty: Finding path plays vital role in network-based systems. Planning largest route essential business,...

let $m$ be an $r$-module and $0 neq fin m^*={rm hom}(m,r)$. we associate an undirected graph $gf$ to $m$ in which non-zero elements $x$ and $y$ of $m$ are adjacent provided that $xf(y)=0$ or $yf(x)=0$. weobserve that over a commutative ring $r$, $gf$ is connected anddiam$(gf)leq 3$. moreover, if $gamma (m)$ contains a cycle,then $mbox{gr}(gf)leq 4$. furthermore if $|gf|geq 1$, then$gf$ is finit...